Extreme events come to mind very easily and people overestimate their probability and overweight them in decisionmaking. In this paper we show that rational use of limited cognitive resources can generate these ’availability biases.’ We hypothesize that availability helps people to quickly make good decisions in very risky situations. Our analysis shows that agents who decide by simulating a finite number of possible outcomes (sampling) should over-sample outcomes with extreme utility. We derive a cognitive strategy with connections to fast-and-frugal heuristics, and we experimentally confirm its prediction that an event’s extremity increases the factor by which people overestimate its frequency. Our model also explains three context effects in decision-making under risk: framing effects, the Allais paradox, and preference reversals.